+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/btpredstaralt_8.ma".
+include "basic_2/computation/fpbs_fpbs.ma".
+
+(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
+
+(* Note: alternative definition of fpbs *)
+definition fpbsa: ∀h. sd h → tri_relation genv lenv term ≝
+ λh,g,G1,L1,T1,G2,L2,T2.
+ ∃∃L,T. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L, T⦄ & ⦃G2, L⦄ ⊢ T ➡*[h, g] T2 & ⦃G2, L⦄ ⊢ ➡*[h, g] L2.
+
+interpretation "'big tree' parallel computation (closure) alternative"
+ 'BTPRedStarAlt h g G1 L1 T1 G2 L2 T2 = (fpbsa h g G1 L1 T1 G2 L2 T2).
+
+(* Main inversion lemmas ****************************************************)
+
+theorem fpbsa_inv_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2.
+ ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 *
+/4 width=5 by fpbs_trans, fsups_fpbs, cpxs_fpbs, lpxs_fpbs/
+qed-.